Offset mortgages and current account mortgages are similar in that they use monies in current accounts or saving accounts to reduce monthly mortgage payments. However, they work in slightly different ways.
With an offset mortgage your, your main bank account or savings account (or both accounts) are linked to your mortgage. These accounts are normally also with your lender. The way they work is that the amount you owe on your mortgage is reduced by the amounts held in these accounts before calculating the interest due. As the amounts held in your bank accounts rises or falls, you are charged less or more interest on your mortgage accordingly.
For example if you have an 'interest only' mortgage of £100,000 and savings or a current account balance of £25,000, then you are charged 'interest' on the remaining £75,000 only. If the difference between the mortgage and bank accounts changes, then the interest charged will change.
Often, monthly payments will remain at an equal amount and 'overpayments' are used to reduce the overall mortgage debt. This is how you can pay off your mortgage early and save money with an offset mortgage. Some lenders will amend the monthly mortgage payment instead so that you benefit from lower payments but, of course, you won't be able to pay off your mortgage early.